(a) On which factors does the resistance of a conductor depend? Define resistivity and state its SI unit.
(b) Give the value of total resistance and total current flowing in the given circuit.

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Solution

(a) The resistance of a conductor depends on thickness (cross sectional area of the wire), length and temperature.
Resistivity is defined as the measure of the resisting power of a specified material to the flow of an electric current.
$R = ρ \frac{l}{A}$
where $R$ = Resistance of the conductor
$ρ$ = Resistivity of the conductor
$l$ = length of the conductor
$A$ = Area of cross section
i.e., $ρ = R \frac{A}{l}$
Unit of resistivity is $Ω m$ .

(b) In the given circuit, the two $2 Ω$ resistors are in series with each other and these resistors are in parallel with other two $2 Ω$ resistors which are in series with each other.

$R_{1} = 2 + 2 = 4 Ω$
$R_{2} = 2 + 2 = 4 Ω$
Total resistance, $R = \frac{R_{1} \times R_{2}}{R_{1} + R_{2}} = \frac{4 \times 4}{4 + 4} = 2 Ω$

Total current flowing in the circuit, $I = \frac{V}{R} = \frac{6}{2} = 3 A$

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(a) On which factors does the resistance of a conductor depend? Define resistivity and state its SI unit.(b) Give the value of total resistance and total current flowing in the given circuit.

(a) On which factors does the resistance of a conductor depend? Define resistivity and state its SI unit.
(b) Give the value of total resistance and total current flowing in the given circuit.